Mu Applications Solutions
2007 Mu Alpha Theta National Convention
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1. B - The velocity of the rock in the x-direction is = 50 and the y-direction is. At t = 2 the total magnitude of velocity is .
2. B - Average rate at which the pages are viewed is =
3. C - Volume =
4. A - ,
5. C – Base of roof has equation .
Base of triangle = 2y, height of triangle is y
Volume of roof =
6. C - ,
7. D – Total Area = 77/60
x / 0 / 1/2 / 1 / 3/2f(x) / 1 / 2/3 / 1/2 / 2/5
Area of Rectangle / 1/2 / 1/3 / 1/4 / 1/5
8. A - ,
9. D - The particles speed is increasing when both velocity and acceleration are both positive or both negative. , . Velocity is positive and negative on . Acceleration is negative and positive when . Speed will be increasing on the intervals .
10. B - , .
,
11. C - ,. Surface Area =
Cost = Minimize cost by taking derivative and setting equal to 0: , r = 3. Cost = 162π
12. A - .
1st 64 feet; , , .
2nd 64 feet; , ,
1st – 2nd
13. B - ,
14. B- Average rate will just be slope from .
15. C - Volume =
16. D -
when ,
when ,
when
17. E - slope of tangent line is which makes an angle of 60 degrees with the horizontal.
slope of makes a slope of 30 degrees with the horizontal. The difference in the angles is 30 degrees and cos (30) is .
18. C- SA
19. C -
. speed =
20. A -
x = 0 is min, x = 40 is maximum
21. A – Area =
22. B - =
23. A -
24. A -
Maximize y = 0, 15, 25
0 and 25 yield minimums so y = 15 and x =10. 15-10 = 5
25.C- Use to approximate.
26. B - . Separate variables and integrate:
Given
Particular solution:
27. B - A= =
28. C - The center of the ellipse is (-9,5) and is 9 units from the y-axis. a = 5 and b = 4. The area of the ellipse is . Use Pappus:
29. E - f(x)=g(x) Curves intersect at 0,1,2
Area = =
30. D - r = 6
The area of the trapezoid equals the sum of the area of the 3 triangles.
A(x),=
A’(x) = , A’(x) = = 0
solve for x, x = 3.
Area of trap =